Question: Solve for $x$ : $2\sqrt{x} + 1 = 10\sqrt{x} + 3$
Answer: Subtract $2\sqrt{x}$ from both sides: $(2\sqrt{x} + 1) - 2\sqrt{x} = (10\sqrt{x} + 3) - 2\sqrt{x}$ $1 = 8\sqrt{x} + 3$ Subtract $3$ from both sides: $1 - 3 = (8\sqrt{x} + 3) - 3$ $-2 = 8\sqrt{x}$ Divide both sides by $8$ $\frac{-2}{8} = \frac{8\sqrt{x}}{8}$ Simplify. $-\dfrac{1}{4} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.